Circumference: Difference between revisions

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The ratio of the circle's circumference to its radius is equivalent to <math>2\pi</math>.{{efn|The Greek letter {{tau}} (tau) is sometimes used to represent [[Tau (mathematical constant)|this constant]]. This notation is accepted in several online calculators<ref name="Desmos">{{cite web |title=Supported Functions |url=https://help.desmos.com/hc/en-us/articles/212235786-Supported-Functions |access-date=2024-10-21 |website=help.desmos.com |url-status=live |archive-url=https://web.archive.org/web/20230326032414/https://help.desmos.com/hc/en-us/articles/212235786-Supported-Functions |archive-date=2023-03-26}}</ref> and many programming languages.<ref name="Python_370">{{cite web |title=math — Mathematical functions |work=Python 3.7.0 documentation |url=https://docs.python.org/3/library/math.html#math.tau |access-date=2019-08-05 |url-status=live |archive-url=https://web.archive.org/web/20190729033443/https://docs.python.org/3/library/math.html |archive-date=2019-07-29}}</ref><ref name="Java-docs">{{cite web |title=Math class |website=Java 19 documentation |url=https://docs.oracle.com/en/java/javase/19/docs/api/java.base/java/lang/Math.html#TAU}}</ref><ref name="Rust">{{cite web |title=std::f64::consts::TAU - Rust |url=https://doc.rust-lang.org/stable/std/f64/consts/constant.TAU.html |access-date=2024-10-21 |website=doc.rust-lang.org |url-status=live |archive-url=https://web.archive.org/web/20230718194313/https://doc.rust-lang.org/stable/std/f64/consts/constant.TAU.html |archive-date=2023-07-18}}</ref>}} This is also the number of [[radian]]s in one [[Turn_(angle)|turn]]. The use of the mathematical constant {{pi}} is ubiquitous in mathematics, engineering, and science.

In ''[[Measurement of a Circle]]'' written circa 250 BCE, [[Archimedes]] showed that this ratio (written as <math>C/d,</math> since he did not use the name {{pi}}) was greater than 3{{sfrac|10|71}} but less than 3{{sfrac|1|7}} by calculating the perimeters of an inscribed and a circumscribed regular polygon of 96 sides.<ref>{{citation|first=Victor J.|last=Katz|title=A History of Mathematics / An Introduction|edition=2nd|year=1998|publisher=Addison-Wesley Longman|isbn=978-0-321-01618-8|page=[https://archive.org/details/historyofmathema00katz/page/109 109]|url-access=registration|url=https://archive.org/details/historyofmathema00katz/page/109}}</ref> This method for approximating {{pi}} was used for centuries, obtaining more accuracy by using polygons of larger and larger number of sides. The last such calculation was performed in 1630 by [[Christoph Grienberger]] who used polygons with 10<sup>40</sup> sides.

In ''[[Measurement of a Circle]]'' written circa 250 BCE, [[Archimedes]] showed that this ratio (written as <math>C/d,</math> since he did not use the name {{pi}}) was greater than 3{{sfrac|10|71}} but less than 3{{sfrac|1|7}} by calculating the perimeters of an inscribed and a circumscribed regular polygon of 96 sides.<ref>{{citation|first=Victor J.|last=Katz|author-link=Victor J. Katz|title=A History of Mathematics / An Introduction|edition=2nd|year=1998|publisher=Addison-Wesley Longman|isbn=978-0-321-01618-8|page=[https://archive.org/details/historyofmathema00katz/page/109 109]|url-access=registration|url=https://archive.org/details/historyofmathema00katz/page/109}}</ref> This method for approximating {{pi}} was used for centuries, obtaining more accuracy by using polygons of larger and larger number of sides. The last such calculation was performed in 1630 by [[Christoph Grienberger]] who used polygons with 10<sup>40</sup> sides.

== Ellipse ==

@@ Line 26: / Line 26: @@
 The ratio of the circle's circumference to its radius is equivalent to <math>2\pi</math>.{{efn|The Greek letter {{tau}} (tau) is sometimes used to represent [[Tau (mathematical constant)|this constant]]. This notation is accepted in several online calculators<ref name="Desmos">{{cite web |title=Supported Functions |url=https://help.desmos.com/hc/en-us/articles/212235786-Supported-Functions |access-date=2024-10-21 |website=help.desmos.com |url-status=live |archive-url=https://web.archive.org/web/20230326032414/https://help.desmos.com/hc/en-us/articles/212235786-Supported-Functions |archive-date=2023-03-26}}</ref> and many programming languages.<ref name="Python_370">{{cite web |title=math — Mathematical functions |work=Python 3.7.0 documentation |url=https://docs.python.org/3/library/math.html#math.tau |access-date=2019-08-05 |url-status=live |archive-url=https://web.archive.org/web/20190729033443/https://docs.python.org/3/library/math.html |archive-date=2019-07-29}}</ref><ref name="Java-docs">{{cite web |title=Math class |website=Java 19 documentation |url=https://docs.oracle.com/en/java/javase/19/docs/api/java.base/java/lang/Math.html#TAU}}</ref><ref name="Rust">{{cite web |title=std::f64::consts::TAU - Rust |url=https://doc.rust-lang.org/stable/std/f64/consts/constant.TAU.html |access-date=2024-10-21 |website=doc.rust-lang.org |url-status=live |archive-url=https://web.archive.org/web/20230718194313/https://doc.rust-lang.org/stable/std/f64/consts/constant.TAU.html |archive-date=2023-07-18}}</ref>}} This is also the number of [[radian]]s in one [[Turn_(angle)|turn]]. The use of the mathematical constant {{pi}} is ubiquitous in mathematics, engineering, and science.
-In ''[[Measurement of a Circle]]'' written circa 250 BCE, [[Archimedes]] showed that this ratio (written as <math>C/d,</math> since he did not use the name {{pi}}) was greater than 3{{sfrac|10|71}} but less than 3{{sfrac|1|7}} by calculating the perimeters of an inscribed and a circumscribed regular polygon of 96 sides.<ref>{{citation|first=Victor J.|last=Katz|title=A History of Mathematics / An Introduction|edition=2nd|year=1998|publisher=Addison-Wesley Longman|isbn=978-0-321-01618-8|page=[https://archive.org/details/historyofmathema00katz/page/109 109]|url-access=registration|url=https://archive.org/details/historyofmathema00katz/page/109}}</ref> This method for approximating {{pi}} was used for centuries, obtaining more accuracy by using polygons of larger and larger number of sides. The last such calculation was performed in 1630 by [[Christoph Grienberger]] who used polygons with 10<sup>40</sup> sides.
+In ''[[Measurement of a Circle]]'' written circa 250 BCE, [[Archimedes]] showed that this ratio (written as <math>C/d,</math> since he did not use the name {{pi}}) was greater than 3{{sfrac|10|71}} but less than 3{{sfrac|1|7}} by calculating the perimeters of an inscribed and a circumscribed regular polygon of 96 sides.<ref>{{citation|first=Victor J.|last=Katz|author-link=Victor J. Katz|title=A History of Mathematics / An Introduction|edition=2nd|year=1998|publisher=Addison-Wesley Longman|isbn=978-0-321-01618-8|page=[https://archive.org/details/historyofmathema00katz/page/109 109]|url-access=registration|url=https://archive.org/details/historyofmathema00katz/page/109}}</ref> This method for approximating {{pi}} was used for centuries, obtaining more accuracy by using polygons of larger and larger number of sides. The last such calculation was performed in 1630 by [[Christoph Grienberger]] who used polygons with 10<sup>40</sup> sides.
 == Ellipse ==

Circumference: Difference between revisions

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